Fundamental wave extraction based on digital twin data-driven technology to improve source multiplication online measurement method, system and equipment

Abstract

The fundamental wave extraction improved source multiplication online measurement method, system and equipment based on digital twin data-driven technology relate to the field of subcritical reactivity measurement technology. The aforementioned method includes: establishing a digital twin mapping harmonic expansion model, and using the measured detector count rate as data drive, iteratively correcting the harmonic expansion coefficient in the digital twin mapping harmonic expansion model, obtaining the corrected fundamental wave neutron information, and then applying the improved source multiplication method to obtain absolute reactivity, thereby realizing online measurement of subcritical reactivity. The present invention combines digital twin and data-driven technology, uses the measured detector count rate as data drive, iteratively corrects the harmonic expansion coefficient in the digital twin harmonic expansion model, can realize more accurate extraction of fundamental wave neutron information, thereby can improve the online measurement accuracy of reactivity of wide subcriticality, and realize accurate online measurement of reactivity of wide range subcriticality.

Description

Technical Field

[0001] The present invention relates to the technical field of subcritical reactivity measurement, and in particular to a fundamental wave extraction-improved source multiplication online measurement method, system and equipment based on digital twin data-driven technology. Background Art

[0002] The fundamental challenge in controlling control rod calibration and determining shutdown depth in subcritical marine reactors is measuring subcritical reactivity over a wide range. By comparing factors such as the placement of external neutron sources in marine reactors, the subcritical span from shutdown to criticality, and offline and online measurement methods, the source multiplication method (NSM) and the modified source multiplication method (MSM) offer technical feasibility for online measurement of subcriticality over a wide range in marine reactors.

[0003] The traditional source multiplication method (NSM) is based on the subcritical multiplication theory of the point reactor model and assumes that the neutron fluence rate distribution is defined as the fundamental mode of the neutron diffusion equation and remains unchanged at any subcriticality. However, in actual measurements, the spatial distribution of the steady-state neutron fluence rate in a subcritical system does not follow the fundamental mode and deviates from the fundamental mode more as the subcriticality increases. This results in the NSM method only being able to provide reliable k values ​​when the reactor is very close to criticality. eff (Effective multiplication coefficient of neutrons in nuclear reactors), which can generally only be used for k eff Estimation of changing trends.

[0004] In order to make the NSM method applicable to slightly deeper subcriticality measurements, the academic community proposed the improved source multiplication method (MSM). Compared with the NSM method, the MSM is based on the actual steady-state neutron injection rate of the subcritical system driven by an external source and uses the detector correction factor f D , external neutron source correction factor f S Implicitly combine the detected count rate M with the predicted k eff (usually calculated) forced association in the expectation that M through f D 、f S Correction to get k eff The MSM method improves the accuracy of the NSM method for slightly deeper subcriticality, but this correction method does not reveal the physical nature of the steady-state neutron fluence rate of the subcritical system, which is the superposition of the fundamental wave and the higher-order harmonics: that is, the steady-state neutron fluence rate of the externally driven subcritical system is formed by the direct contribution of the external neutron source, the superposition of the fundamental wave and the higher-order harmonic neutron fluence rate contribution of the subcritical multiplication process, and the contribution of the higher-order harmonics increases with the deepening of subcriticality, causing the steady-state neutron fluence rate to deviate significantly from the fundamental wave distribution. This results in the need for MSM to calculate personalized f for each scheme (different core schemes, different neutron sources, different detector positions). D 、f S, its universality is not strong. Practical applications show that at deeper subcriticality, the k given by MSM eff The error of the measurement results still cannot meet engineering requirements, and it is difficult to use it to accurately measure the subcritical reactivity of marine reactors over a wide range covering deep and shallow subcriticality. Summary of the Invention

[0005] One of the purposes of the present invention is to provide a new method for online measurement of improved source multiplication based on fundamental wave extraction that combines digital twin and data-driven technology, providing an efficient and reliable means for accurate online measurement of wide-range subcritical reactivity of marine reactors.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an improved source multiplication online measurement method based on fundamental wave extraction of digital twin data-driven technology, comprising the following steps:

[0007] A digital twin mapping harmonic expansion model is established, and the measured detector count rate is used as data drive. The harmonic expansion coefficient in the digital twin mapping harmonic expansion model is iteratively corrected to obtain the corrected fundamental neutron information. Then, the improved source multiplication method is applied to obtain the absolute reactivity, thereby realizing online measurement of subcritical reactivity.

[0008] Furthermore, the established digital twin mapping harmonic expansion model is

[0009]

[0010] Among them, φ s,c Mapping the neutron flux of the harmonic expansion model for the digital twin, A i,c is the harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

[0011] Furthermore, using the measured detector count rate as data drive, the harmonic expansion coefficients in the digital twin mapping harmonic expansion model are iteratively corrected to obtain the corrected fundamental neutron information. The specific steps include:

[0012] By using the measured detector count rate as data drive, the detector count rate corresponding to the digital twin mapping harmonic expansion model is corrected, and then the harmonic expansion coefficient is corrected to obtain the corrected fundamental neutron information;

[0013] The detector count rate R corresponding to the harmonic expansion model of the digital twin mapping c for

[0014] R c =φ s,c Σ d

[0015] Among them, φ s,cMapping the neutron flux of the harmonic expansion model for the digital twin, Σ d is the nuclear reaction macroscopic cross section of the neutron detector;

[0016] The measured detector count rate R m for

[0017] R m =φ s,m Σ d

[0018] Among them, φ s,m is the actual measured neutron flux, Σ d is the nuclear reaction macroscopic cross section of the neutron detector;

[0019] Neutron flux φ of the modified digital twin mapping harmonic expansion model s ' ,c for

[0020]

[0021] Among them, A' i,c is the corrected harmonic expansion coefficient, φ i,λ is the neutron fluence rate of the λ eigenvalue of the i-th group.

[0022] Furthermore, the above method further comprises the following steps: extracting the fundamental mode component from the measured neutron count rate:

[0023]

[0024] Among them, M 1,ex is the extracted fundamental mode component, M ex is the measured neutron counting rate, C1 M (r d ) is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector.

[0025] Furthermore, when the improved source multiplication method is applied to obtain absolute reactivity, the absolute reactivity of the subcritical system is calculated according to the following formula:

[0026]

[0027] in, and is the correction factor, Q l is the neutron count multiplication, and the subscript ref is the reference subcritical state, that is, is the absolute reactivity of the reference subcritical state.

[0028] Furthermore, the correction factor for

[0029]

[0030] in, is the characteristic function, s is the external neutron source, and the subscript ref is the reference subcritical state, that is, is the characteristic function of the reference subcritical state.

[0031] Furthermore, the correction factor for

[0032]

[0033] in, is the fundamental neutron fluence rate of the subcritical system, r d is the neutron detector position, Σ d is the macroscopic cross section of nuclear reaction of neutron detector, and the subscript ref is the reference subcritical state, i.e. is the fundamental neutron fluence rate of the reference subcritical state.

[0034] Furthermore, the correction factor for

[0035]

[0036] in, is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector, and the subscript ref is the reference subcritical state, i.e. is the extraction coefficient of the reference subcritical state.

[0037] Another object of the present invention is to provide an online measurement system for fundamental wave extraction and improved source multiplication based on digital twin data-driven technology, which comprises:

[0038] A digital twin model building unit, used to establish a digital twin mapping harmonic expansion model;

[0039] a data driving unit, configured to use the measured detector count rate as data driving;

[0040] A correction unit is used to iteratively correct the harmonic expansion coefficients in the digital twin mapping harmonic expansion model to obtain the corrected fundamental neutron information;

[0041] Computational unit for obtaining absolute reactivity using the modified source multiplication method.

[0042] The system may further include a fundamental wave extraction unit configured to extract a fundamental wave mode component from the measured neutron count rate.

[0043] In addition, the present invention also provides a fundamental wave extraction improved source multiplication online measurement device based on digital twin data-driven technology, which includes:

[0044] memory for storing computer programs;

[0045] A processor is used to implement the steps of the above-mentioned fundamental wave extraction and improved source multiplication online measurement method based on digital twin data-driven technology when executing the computer program.

[0046] The present invention is based on an improved source multiplication method based on the fundamental wave extraction method, combines digital twin and data-driven technology, uses the experimentally measured detector count rate as data drive, and iteratively corrects the harmonic expansion coefficient in the digital twin harmonic expansion model to make it consistent with the fundamental wave neutron information of a real typical experimental device, thereby achieving more accurate extraction of fundamental wave neutron information, thereby improving the online measurement accuracy of reactivity over a wide subcriticality range, and achieving accurate online measurement of reactivity over a wide subcriticality range, which can provide an efficient and reliable means for accurate online measurement of subcritical reactivity over a wide range of marine reactors. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Flowchart for iterative correction of harmonic expansion model for digital twin data-driven technology. DETAILED DESCRIPTION

[0048] In order to facilitate those skilled in the art to better understand the improvements of the present invention relative to the prior art, the present invention is further described below with reference to the accompanying drawings and embodiments.

[0049] Reactivity reflects the neutron multiplication characteristics of neutrons in a reactor when they are distributed according to fundamental wave characteristics. To achieve accurate measurement, traditional wide-range subcritical reactivity online measurement methods: source multiplication method (NSM) and improved source multiplication method (MSM) require accurate extraction of fundamental wave information from the steady-state neutron fluence rate superimposed by the fundamental wave and higher-order harmonics. In addition, a new improved source multiplication method based on fundamental wave extraction should be developed.

[0050] In the eigenvalue problem of the neutron balance equation, harmonics and conjugate harmonics are in a biorthogonal relationship, providing comprehensive mathematical properties for extracting fundamental information. A new improved source multiplication method based on fundamental extraction must consider factors such as fundamental mode extraction, neutron value perturbations, and spatial effect corrections. Furthermore, due to discrepancies between the physical model and the actual device during harmonic calculation, numerical uncertainty factors such as nuclear data will also affect the accuracy of fundamental extraction. Therefore, it is necessary to establish an accurate and reliable physical model that can reflect the true state of subcritical reactors.

[0051] Digital twinning is a technology that maps physical systems to digital models in cyberspace. Data-driven digital twinning uses actual detector output data to feed back into the reconstructed calculation results of higher-order harmonics of the steady-state neutron fluence rate. Data assimilation is used to correct theoretical calculation results, effectively avoiding the uncertainties introduced by theoretical modeling and numerical calculations. This improves computational accuracy and ensures that the fundamental wave extraction results more accurately reflect the neutronic properties of the actual object. Therefore, combining digital twinning with data-driven methods to accurately extract fundamental wave information from the steady-state neutron fluence rate, which is a superposition of the fundamental wave and higher-order harmonics, and establishing a new improved source multiplication method based on fundamental wave extraction, can provide an efficient and reliable means for accurate online measurement of subcritical reactivity over a wide range in marine reactors.

[0052] Based on the above concept, the present invention provides a new method for online measurement of subcritical reactor reactivity over a wide range (i.e., a new method for online measurement of fundamental wave extraction and improved source multiplication based on digital twin data-driven technology), which can realize high-efficiency and accurate calibration of ship reactor control rods and online measurement of shutdown depth of deep subcritical reactors, and has important theoretical value and engineering significance for reactor physics and experimental technology.

[0053] The details are as follows:

[0054] The high-order harmonics and conjugate harmonics have biorthogonal characteristics. The neutron flux rate for any working condition can be expanded into the following expression:

[0055]

[0056] Among them A n is the expansion coefficient, which is related to the proliferation characteristics and exogenous characteristics of the deep subcritical system driven by a steady-state external source, and can be obtained through harmonic and conjugate harmonic calculations. For the calculation method of high-order harmonics, deterministic methods or Monte Carlo methods can be used.

[0057] From formula (1), we can see that the neutron flux rate is expanded into the following form:

[0058]

[0059] Among them, φ i,λ represents the neutron fluence rate of the λ eigenvalue of the i-th group.

[0060] In order to distinguish the neutron flux rate of the digital twin mapping model from the experimentally measured neutron flux rate, the neutron flux of the digital twin mapping model is defined as: s,c , the experimentally measured real neutron flux is: φ s,realThe digital twin mapping model and the experimentally measured real neutron flux are driven by the detector count rate as data, thereby realizing the mutual iterative correction of the neutron injection rate of the digital twin mapping model and the experimentally measured real neutron flux, where the detector count rate R corresponding to the digital twin mapping model is c and the detector count rate R obtained from experimental measurements m The definition is as follows:

[0061] R c =φ s,c Σ d (3)

[0062] R m =φ s,m Σ d (4)

[0063] Among them, φ s,m is the experimentally measured neutron flux, Σ d is the macroscopic cross section of nuclear reactions in the neutron detector.

[0064] By R m (Experimental measurement value) as data driver, and then R c Make corrections, that is, correct the harmonic expansion coefficient A i,c , the corrected harmonic expansion coefficient can be defined as A' i,c , so the corrected calculated value is:

[0065]

[0066] Among them, φ s ' ,c Mapping model neutron flux for the revised digital twin.

[0067] At this time, the fundamental neutron information obtained by formula (5) can be considered to be almost consistent with the fundamental neutron information obtained in the experiment. Then, the improved source multiplication method is applied to obtain the absolute reactivity. The absolute reactivity obtained at this time can truly express the subcriticality of the actual core. That is, by establishing a digital twin mapping harmonic expansion model and using the measured detector count rate as data drive, the digital twin harmonic model and the typical experimental device are iteratively corrected to correct the harmonic expansion coefficient, so that the corrected fundamental neutron information can truly reflect the subcriticality of the typical experimental device. The relevant interactive process is as follows: Figure 1 shown.

[0068] To realize the above overall process, how to extract fundamental information from complex detector information is a key issue. Therefore, the steady-state neutron diffusion equation of the subcritical system with an external neutron source can be described as:

[0069] Lφ s (r)=Fφ s(r)+s(r) (6)

[0070] Where L is the neutron disappearance operator, F is the neutron production operator, and s(r) is the external neutron source. Subcritical systems can also be analyzed using the neutron diffusion equation of the eigenvalue problem:

[0071]

[0072] Among them, k i is the i-th eigenvalue, φ i c is the corresponding characteristic function. It is known that the maximum characteristic value of the above formula is "neutron multiplication factor (k eff )”, the corresponding characteristic function is the fundamental mode. For the eigenvalue problem of formula (6), its conjugate equation is defined as follows:

[0073]

[0074] in and is the conjugate operator of L and F; is the same as the eigenvalue k i The associated i-th adjoint characteristic function. and The orthogonal relationship is as follows:

[0075]

[0076] in Defined as:

[0077]

[0078] The superscript "T" represents the transpose of a matrix or vector, and the integration is performed over the entire region of the neutron multiplication system. i c and As a complete set, the neutron fluence rate distribution φ of the fixed source problem s It can be expanded into formula (1) using characteristic function. i Is the expansion coefficient. Expansion coefficient A i The neutron generation operator F can be combined from the left side of equation (1) to both sides of equation (1), and the inner product defined by equation (11) can be applied to obtain the following result:

[0079]

[0080] Therefore, the neutron fluence rate distribution φ s The characteristic function φ can be used i c Expand, such as:

[0081]

[0082] In order to s Extract the fundamental mode and introduce the subgroup coefficient C of the g group s 1,g (r), as follows:

[0083]

[0084] in, is the fundamental neutron fluence rate of the gth group of the subcritical system, is the g-th group neutron fluence rate of the subcritical system with an external neutron source.

[0085] in and is the g-group flux distribution normalized by the total number of fission neutrons, such as:

[0086]

[0087] The neutron count rate M(r d ) and the fundamental mode component (M1) contained in M ​​can be expressed as:

[0088] M(r d )=Σ d φ s (r d ) (16)

[0089]

[0090] where r d is the position of the neutron detector. Symbol Σ d and C1 s represents a row vector with G elements and is defined as a diagonal matrix with G diagonal elements:

[0091] Σ d =[ε1Σ d,1 ,…,ε G Σ d,G ] (18)

[0092]

[0093] Among them, Σ d,g is the macroscopic cross section of the neutron detection nuclear reaction of the g-th group neutrons, ε g is the detector efficiency of the nuclear detection process caused by the g-th group neutrons, is the neutron group coefficient of the Gth group.

[0094] The extraction coefficients for extracting the fundamental mode components from the measured data are defined as:

[0095]

[0096] And the coefficient C1 M (r d ) can be calculated in advance based on the numerical analysis of equations (7) and (8). Then the neutron counting rate (M) obtained from the actual measurement is ex ) contains the fundamental mode component (M 1,ex ) can be extracted as:

[0097]

[0098] In summary, combined with digital twin data-driven technology, the experimental detector count rate is used as data drive to iteratively correct the A in the digital twin harmonic expansion model. i,c , which makes it consistent with the fundamental neutron information of a real typical experimental device. The new improved source multiplication method based on the fundamental wave extraction method proposed in the present invention can achieve more accurate extraction of fundamental wave neutron information.

[0099] In order to measure the reactivity of subcritical systems, d A reference subcritical state is designated at , and a neutron detector is placed. It is assumed that the intensity of the external neutron source remains constant in any subcritical state. Problems with variable intensity can also be handled by some minor modifications to the following procedure. The fundamental mode component M contained in the measurement data 1,ref Related to subcriticality, as follows:

[0100]

[0101] The subscript "ref" is called the reference subcritical state. The neutron count multiplication Q in the first subcritical state l Can be defined as

[0102]

[0103] For neutron count multiplication Q l , the following three correction factors are introduced:

[0104]

[0105] Where s is the external neutron source, is the fundamental neutron fluence rate of the subcritical system, Σ d is the macroscopic cross section of nuclear reactions in the neutron detector.

[0106] Using these correction factors, the reactivity of the subcritical system can be obtained for:

[0107]

[0108] The change in reactivity disturbs the neutron important field and the neutron flux distribution, causing the fundamental mode intensity contained in the neutron source to Changes in fundamental mode The distribution of has also changed. From equations (24), (25) and (26), we can see that Related to the extraction of fundamental modes, Corrected the effects caused by neutron important field perturbations, Corrected spatial effects caused by fundamental mode perturbations.

[0109] In the traditional MSM method, instead of using three correction factors and Instead, we use two factors f s and f ε To correct the subcriticality. These two factors can be expressed by the three correction coefficients mentioned above as follows:

[0110]

[0111]

[0112] From the above expression, we can find that in the traditional MSM method, f is defined as the “detector efficiency”. ε is decomposed into two correction factors, one for fundamental mode extraction and one for spatial correction. These correction factors vary in a very complex way, depending on the reactivity addition method, the geometry of the neutron multiplication system, the position of the neutron detectors, and the distribution of the external neutron source. Therefore, f, which is a combination of the two factors, ε The changes will become more complex. From this perspective, compared with traditional methods, the new method proposed in this invention can evaluate the effects of each correction individually and in detail, and through these analyses, provide a clear physical explanation of the correction process. In addition, the present invention combines digital twin data-driven technology, using the experimental detector count rate as the data driver, to achieve more accurate extraction of fundamental neutron information, thereby improving the accuracy of online reactivity measurement over a wide subcritical range.

[0113] The above embodiments are preferred implementation schemes of the present invention. In addition, the present invention can also be implemented in other ways. Any obvious replacement without departing from the concept of the present technical solution is within the scope of protection of the present invention.

Claims

1. The fundamental wave extraction and improved source multiplication online measurement method based on digital twin data-driven technology is characterized by: The following steps are involved: A digital twin mapping harmonic expansion model is established. Using the measured detector count rate as data driver, the harmonic expansion coefficients in the digital twin mapping harmonic expansion model are iteratively corrected to obtain the corrected fundamental neutron information. An improved source multiplication method is then applied to obtain absolute reactivity, thereby enabling online measurement of subcritical reactivity. Among them, the established digital twin mapping harmonic expansion model is ； in, Mapping the neutron flux of the harmonic expansion model for the digital twin, A i,c is the harmonic expansion coefficient, is the neutron fluence rate of the λ eigenvalue of the i-th group.

2. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: Using the measured detector count rate as data drive, the harmonic expansion coefficients in the digital twin mapping harmonic expansion model are iteratively corrected to obtain the corrected fundamental neutron information. The specific steps include: By using the measured detector count rate as data drive, the detector count rate corresponding to the digital twin mapping harmonic expansion model is corrected, and then the harmonic expansion coefficient is corrected to obtain the corrected fundamental neutron information; The digital twin maps the detector count rate corresponding to the harmonic expansion model R c for ； in, Mapping the neutron flux of the harmonic expansion model for the digital twin, Σ d is the nuclear reaction macroscopic cross section of the neutron detector; Measured detector count rate R m for ； in, is the actual measured neutron flux, Σ d is the nuclear reaction macroscopic cross section of the neutron detector; Modified digital twin mapping neutron flux of the harmonic expansion model for ； in, A ' i,c is the corrected harmonic expansion coefficient, is the neutron fluence rate of the λ eigenvalue of the i-th group.

3. The fundamental wave extraction improved source multiplication online measurement method based on digital twin data-driven technology according to claim 1 is characterized in that: The following steps are also included: Extract the fundamental mode component from the measured neutron count rate: ； in, M 1,ex is the extracted fundamental mode component, M ex is the measured neutron counting rate, C 1 M ( r d ) is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector.

4. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 1 is characterized in that: When the improved source multiplication method is used to obtain absolute reactivity, the absolute reactivity is calculated according to the following formula: : ； in, is the correction factor for the effects caused by the neutron important field disturbance, is the correction factor for the spatial effect caused by the fundamental mode disturbance, is the correction factor related to the extraction of the fundamental mode, is the neutron count multiplication in the first subcritical state, and the subscript ref is the reference subcritical state.

5. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 4 is characterized in that: The correction factor for ； in, is the characteristic function, s is the external neutron source, and the subscript ref is the reference subcritical state.

6. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 4 is characterized in that: The correction factor for ； in, is the fundamental neutron fluence rate of the subcritical system, r d is the neutron detector position, Σ d is the nuclear reaction macroscopic cross section of the neutron detector, and the subscript ref is the reference subcritical state.

7. The method for fundamental wave extraction and improved source multiplication online measurement based on digital twin data-driven technology according to claim 4 is characterized in that: The correction factor for ； in, is the extraction coefficient for extracting the fundamental mode component, r d is the position of the neutron detector, and the subscript ref is the reference subcritical state.

8. A fundamental wave extraction and improved source multiplication online measurement system based on digital twin data-driven technology, used to implement the fundamental wave extraction and improved source multiplication online measurement method based on digital twin data-driven technology as described in any one of claims 1 to 7, characterized in that: include: A digital twin model building unit, used to establish a digital twin mapping harmonic expansion model; a data driving unit, configured to use the measured detector count rate as data driving; A correction unit is used to iteratively correct the harmonic expansion coefficients in the digital twin mapping harmonic expansion model to obtain the corrected fundamental neutron information; Computational unit for obtaining absolute reactivity using the modified source multiplication method.

9. Fundamental wave extraction and improved source multiplication online measurement equipment based on digital twin data-driven technology, characterized by: include: Memory for storing computer programs; A processor is used to implement the steps of the fundamental wave extraction improved source multiplication online measurement method based on digital twin data-driven technology as described in any one of claims 1 to 7 when executing the computer program.

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